Honsberger R. — Mathematical diamonds :: Электронная библиотека попечительского совета мехмата МГУ

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Honsberger R. — Mathematical diamonds

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Название: Mathematical diamonds

Автор: Honsberger R.

Аннотация:

Ross Honsberger has done it again. He has brought together another wonderful collection of elementary mathematical problems and their solutions abounding in striking surprises and brilliant ideas that reflect the beauty of mathematics. Many of these problems come from mathematical journals. Others come from various mathematical competitions such as the Tournament of the Towns, the Balkan Olympiad, the American Invitational Mathematics Exam, and the Putnam exam. And, of course, there is a problem suggested by Paul Erd?s. This book is ideal for students, teachers and anyone interested in recreational mathematics.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 255

Добавлена в каталог: 11.09.2015

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Предметный указатель

A certain angle bisector in a parallelogram      21
A certain quartic equation with an integer root      7
A certain rectangle and the relation $d^{2/3} - n^{2/3} = 1$       14
A certain set of equal circles in a square      8
A cevian property      15
A construction problem on perpendicular medians      11
A function f such that $f(i) \neq f(j)$ whenever |i — j| is a prime      22
A locus of midpoints of segments between two circles      7
A property involving the median of a triangle      8
A property of 16-digit integers      11
A property of cevian conjugates      15
A property of isosceles triangles      5
A property of regular n-gons inscribed in a unit circle      19
A property of sequences of positive integers      8
A property of the medial triangle      18
A property of uncountable sets of real numbers      18
A quadratic equation involving [x], the integer part of x      5
A sequence of positive integers $\{a_{k}\}$ with $k | a_{1} + a_{2} + ... + a_{k}$       8
A set of three quatioiis involving x, [x], {x}, etc.      8
A special concurrency and collinearity      15
A variation on a problem of Regiomontanus      11
Algebraic integer      13
An "oasis" property of prime numbers      20
An inequality on a sum of reciprocals and the rth prime      5
Analytic geometry      24
Arithmetic mean-geometric mean inequality      8
Binomial theorem      4
Brown, Steve      3
Bull, John      19
Butterfly problem      16
Cevian, cevian conjugate, cevian property, Ceva's theorem      15
Chebyshev polynomial      13
Circumcenter of a triangle      5 22
Coin-tossing: odd man wins      12
Coloring lattice points      13
Complete graph      6
Countability of the rationals      18
Covering 1, 1/2, 1/3,... with five bars      14
De Moivre's theorem      4
Differentiation      7
Dilatation (Homothecy)      7 22
Dinh, Hung      1
Dirichlet's theorem      20
Dissecting a 2 by 10 rectangle to cover a square      5
Distance-rate-time problem      8
Ellipse; given foci, tangent to x-axis; find major axis      5
Erdoes' result on infinite sets and integral distances      4
Erdoes' theorem on big distances in sets of diameter $\leq 1$       6
Establish $\Delta = Rs$ , where s = semiperimeter of the orthic triangle      5
Euclid      19
Euler line      22
Farey sequences      8
Fejer, Leopold      5
Find lattice points on graph of $x^{2} - 3xy - 13x + 5y + 11 = 0$       14
Finding terms that are divisible by 11 in a certain sequence      22
Fractional part of an integer      8
Generating function      17
Graph, linear      3
Hahn, Liong-shin      11
Haruki, Hiroshi      16
Homothecy (Dilatation)      7 22
Hyperbola      4
Induction      8 10 17 20
Inequality concerning prime numbers      9
Infinite decimals      20
Infinite product      17
Inscribed circles      23
Integer distances      4
Interlocking sequences      8
Lambek, Joseph      17

Law of Cosines      6
Law of Sines      21
Leapfrog induction      20
Linear dependence      5
Markov chain      12
Marquez, Juan-Bosco Romero      15
Matrix, 0-1      5
Mendelsohn, Nathan      20
Menelaus' theorem      15
Minimum circle enclosing a set of points in the plane      11
Moser, Leo      17
Mr. A thinks of a number      11
Number of divisors of an integer      11
On $n = a_{0} + a_{1} \cdot 2 + a_{2} \cdot 2^{2} + ... + a_{k} \cdot 2^{k}, a_{i} \in \{0, 1, 2\}$       8
On 16 positive integers with sum 100 and sum of squares 1000      14
On a certain square in a circle      21
On a certain triangle of maximum area      21
On certain fractions that reduce to integers      8
On certain triangles which have a common Euler line      22
On circles capturing $\geq [n/3]$ points of a set of n planar points      11
On multiples of 24      7
On prime decompositions and a perfect square      5
On the functions $x^{2} + y + 2$ and $y^{2} + 4x$       11
On the largest regular hexagon inscribed in a square      11
On the minimum value of a certain function      11
On the triangle formed from the medians of a triangle      11
On three cards marked with integers x, y, z      11
Orthic triangle      5 22
Orthocenter of a triangle      22
Packing two squares into a third square      7
Payan, Charles      1
Polynomial; coefficients $a_{0}$ , $a_{n}$ , odd implies no rational root      5
Pythagorean triple      4
Quadratic f(x) consists only of 1's when x consists only of 1's      8
Quartering a quadrilateral; segments to midpoints of sides      5
Rabinowitz, Stanley      5
Random points      3
Rank of a matrix      5
Recursion      8 12
Reflecting a side of a triangle in the other two sides      5
Reflection of the plane      5 16
Reflector property of the ellipse      5
Relatively prime integers      9
Root-mean-square inequality      14
Rotation of coordinate axes      24
Rotation of the plane      5 8
Sedinger, Harry      11
Sharygin, I.F.      8
Sierpinski, Waclaw      20
Silverman, David      4
Special properties of 30 and 24      9
Square-free part of an integer      5
Subdividing a convex quadrilateral into $n^{2}$ sub-quadrilaterals      25
Takeda, Shingen      23
Takeda, Shinko      23
Tanaka, Shotaro      23
The 37th digit in a certain decimal      20
The butterfly problem      16
The footrace      5
The fractions on either side of 5/8      8
The greatest integer value of $\sqrt{x - 174} + \sqrt{x + 34}$       14
The method of infinite descent      20
The remarkable point Q      16
The Schwab — Schoenberg mean      8
The strolling professor and her assistant      8
The value of $sin \theta — cos \theta$ for a certain $\theta$       14
The weight of watermelons      8
To construct an isosceles triangle to touch two given circles      8
Vector, geometric      13
Winterle, Riko      18

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